Large elastic deformations of soft solids up to failure: new hyperelastic models with error estimation

A direct approach is proposed to obtain new multi-axial elastic potentials for incompressible soft solids. Results are presented with novelties in three respects, namely (i) any given benchmark test data for three deformation modes may be exactly fitted, including uniaxial, equi-biaxial, and plane-strain extension; (ii) model parameters of direct physical meanings may be provided to represent both the strain-stiffening effect and failure behavior; and (iii) error estimation may be established for all possible deformation modes. Numerical examples are in good agreement with Treloar’s classic data for rubbers and with extensive data for gellan gels up to failure.